16,606 research outputs found
On the predictive power of Local Scale Invariance
Local Scale Invariance (LSI) is a theory for anisotropic critical phenomena
designed in the spirit of conformal invariance. For a given representation of
its generators it makes non-trivial predictions about the form of universal
scaling functions. In the past decade several representations have been
identified and the corresponding predictions were confirmed for various
anisotropic critical systems. Such tests are usually based on a comparison of
two-point quantities such as autocorrelation and response functions. The
present work highlights a potential problem of the theory in the sense that it
may predict any type of two-point function. More specifically, it is argued
that for a given two-point correlator it is possible to construct a
representation of the generators which exactly reproduces this particular
correlator. This observation calls for a critical examination of the predictive
content of the theory.Comment: 17 pages, 2 eps figure
A necessary extension of the surface flux transport model
Customary two-dimensional flux transport models for the evolution of the
magnetic field at the solar surface do not account for the radial structure and
the volume diffusion of the magnetic field. When considering the long-term
evolution of magnetic flux, this omission can lead to an unrealistic long-term
memory of the system and to the suppression of polar field reversals. In order
to avoid such effects, we propose an extension of the flux transport model by a
linear decay term derived consistently on the basis of the eigenmodes of the
diffusion operator in a spherical shell. A decay rate for each eigenmode of the
system is determined and applied to the corresponding surface part of the mode
evolved in the flux transport model. The value of the volume diffusivity
associated with this decay term can be estimated to be in the range 50--100
km^2/s by considering the reversals of the polar fields in comparison of flux
transport simulations with observations. We show that the decay term prohibits
a secular drift of the polar field in the case of cycles of varying strength,
like those exhibited by the historical sunspot record.Comment: for further information visit: http://solweb.oma.be/users/baumann
Desensitizing Inflation from the Planck Scale
A new mechanism to control Planck-scale corrections to the inflationary eta
parameter is proposed. A common approach to the eta problem is to impose a
shift symmetry on the inflaton field. However, this symmetry has to remain
unbroken by Planck-scale effects, which is a rather strong requirement on
possible ultraviolet completions of the theory. In this paper, we show that the
breaking of the shift symmetry by Planck-scale corrections can be
systematically suppressed if the inflaton field interacts with a conformal
sector. The inflaton then receives an anomalous dimension in the conformal
field theory, which leads to sequestering of all dangerous high-energy
corrections. We analyze a number of models where the mechanism can be seen in
action. In our most detailed example we compute the exact anomalous dimensions
via a-maximization and show that the eta problem can be solved using only
weakly-coupled physics.Comment: 34 pages, 3 figures
Kinetics of the long-range spherical model
The kinetic spherical model with long-range interactions is studied after a
quench to or to . For the two-time response and correlation
functions of the order-parameter as well as for composite fields such as the
energy density, the ageing exponents and the corresponding scaling functions
are derived. The results are compared to the predictions which follow from
local scale-invariance.Comment: added "fluctuation-dissipation ratios"; fixed typo
Ageing without detailed balance: local scale invariance applied to two exactly solvable models
I consider ageing behaviour in two exactly solvable reaction-diffusion
systems. Ageing exponents and scaling functions are determined. I discuss in
particular a case in which the equality of two critical exponents, known from
systems with detailed balance, does not hold any more. Secondly it is shown
that the form of the scaling functions can be understood by symmetry
considerations.Comment: 6 pages, contribution to the summer school "Ageing and the Glass
Transition" held in Luxemburg in September 05. Published versio
A possible signature of terrestrial planet formation in the chemical composition of solar analogs
Recent studies have shown that the elemental abundances in the Sun are
anomalous when compared to most (about 85%) nearby solar twin stars. Compared
to its twins, the Sun exhibits a deficiency of refractory elements (those with
condensation temperatures Tc>900K) relative to volatiles (Tc<900K). This
finding is speculated to be a signature of the planet formation that occurred
more efficiently around the Sun compared with the majority of solar twins.
Furthermore, within this scenario, it seems more likely that the abundance
patterns found are specifically related to the formation of terrestrial
planets. In this work we analyze abundance results from six large independent
stellar abundance surveys to determine whether they confirm or reject this
observational finding. We show that the elemental abundances derived for solar
analogs in these six studies are consistent with the Tc trend suggested as a
planet formation signature. The same conclusion is reached when those results
are averaged heterogeneously. We also investigate the dependency of the
abundances with first ionization potential (FIP), which correlates well with
Tc. A trend with FIP would suggest a different origin for the abundance
patterns found, but we show that the correlation with Tc is statistically more
significant. We encourage similar investigations of metal-rich solar analogs
and late F-type dwarf stars, for which the hypothesis of a planet formation
signature in the elemental abundances makes very specific predictions. Finally,
we examine a recent paper that claims that the abundance patterns of two stars
hosting super-Earth like planets contradict the planet formation signature
hypothesis. Instead, we find that the chemical compositions of these two stars
are fully compatible with our hypothesis.Comment: To appear in Astronomy and Astrophysic
Ageing in bosonic particle-reaction models with long-range transport
Ageing in systems without detailed balance is studied in bosonic contact and
pair-contact processes with Levy diffusion. In the ageing regime, the dynamical
scaling of the two-time correlation function and two-time response function is
found and analysed. Exact results for non-equilibrium exponents and scaling
functions are derived. The behaviour of the fluctuation-dissipation ratio is
analysed. A passage time from the quasi-stationary regime to the ageing regime
is defined, in qualitative agreement with kinetic spherical models and p-spin
spherical glasses.Comment: Latex2e, 24 pages, with 9 figures include
- …